KR100856379B1 - Determination method of sape annealing matrix of nuclear power plants with genetic algorithm - Google Patents

Abstract

A method for determining a shape annealing matrix of a nuclear power plant using a genetic algorithm is provided to improve safety of a core by detecting a correct solution physically. A method for determining a shape annealing matrix of a nuclear power plant using a genetic algorithm includes the steps of: providing an optimum physical solution based on a genetic algorithm having a limited condition as the equation below. Theta(x,lambda,s,rho)=f(x) - Sigmalambdaisilog(si-ci(x))+ Sigmalambdaici(x)+rho/2Sigmaci(x)^2, wherein the lambda denotes lagrange multiplier vector, lambdai of the lambda is non-negative and lagnrange multiplier estimates, the vector s denotes non-negative shift, the rho denotes a positive penalty parameter, the C(x) is a nonlinear inequality and equality constraints, and the m and mt denote the number of nonlinear inequality constraints and the number of nonlinear constraints respectively.

Description

Determination Method of sape Annealing Matrix Of Nuclear Power Plants With Genetic Algorithm

1 is a conceptual diagram of an off-road instrument of a nuclear power plant according to a preferred embodiment of the present invention.

2 shows the relationship between the out-of-meter instrument signal and the core output distribution.

Figure 3 is a comparison table comparing the error during the cycle by the conventional SAM determination method and the off-site instrument SAM determination method according to the present invention.

The present invention relates to a method for determining a set value (Shape Annealing Matrix, SAM) of an offshore instrument used for core protection of a nuclear power plant. More particularly, the present invention relates to a method for calculating a SAM performed at the beginning of each operating cycle using a genetic algorithm. The present invention relates to a method for determining an external instrument SAM that can greatly improve the accuracy and provide a solution of an area that always has a physical meaning.

In general, nuclear plant designers pre-calculate and provide information on the maximum allowable power that a fuel can withstand, and operators maintain fuel integrity by operating within the maximum allowable power.

The output distribution in the core consists of a radial output distribution and an axial output distribution. The radial output distribution is determined at the design stage according to the fuel assembly loading model that includes the appropriate distribution of the burnable absorber. However, the axial output distribution is difficult to control due to the xenon transition phenomenon. Therefore, the nuclear power plant has set an operating allowance area for the axial output distribution to maintain the nuclear fuel integrity.

In other words, the accuracy of the out-of-counter instrument is very important as it limits the allowable area to the axial output deviation range. Therefore, in order to calculate the output distribution of the reactor as the measurement data of the off-site instrument at the beginning of every cycle, the full power operation is possible after the SAM value is determined and installed using the data measured at the 20-80% output.

In Korea's standard nuclear power plant, three types of off-site instruments such as safety channels, control channels, and start-up channels are installed outside the reactor vessel.

In this case, the safety channel external measuring instrument system is composed of four independent channels, each channel is composed of three sub-channels (TOP, MID, BOT).

The safety channel external measuring instrument signal is very important because it is used as an input of a core protection calculator (CPC), which is a core protection system, to determine the output and output distribution of the core after the SAM value is multiplied.

FIG. 1 schematically illustrates the concept of an offsite instrument of a nuclear power plant, and FIG. 2 schematically illustrates a relationship between the offsite instrument signal and a core output distribution.

As is well known, the signal of the out-of- instruments is mainly dependent on the output of the fuel assembly located outside the core. Thus, the physically out-of-core instrument signal has a closer physical correlation with the core outer power distribution than with the core mean output distribution.

The core protection calculator (CPC) assumes that the upper, middle and lower outputs outside the core have a linear relationship with the upper, middle and lower signals of the outside instrument. A 3x3 matrix of surnames is defined as SAM.

That is, it is assumed that the upper, middle, and lower outputs P _i of the outer periphery have a relation as shown in Equation 1 below with the upper, middle, and lower signals D _i of the external measuring instrument.

Equation 1 is basically an approximate expression, and the actual physical phenomenon should be expressed in a more complicated relationship. As a result, determining the SAM corresponds to mathematically solving the so-called overdetermined problem.

That is, it is necessary to determine the SAM that provides the minimum error for the various out-of-core output distributions and corresponding out-of-core instrument signals.

In other words, in order to determine the SAM, various core output distributions and out-of-core instrument outputs are required. Currently, in the case of Korean standard nuclear power plants, SAM is determined using only measured data, and necessary measurement data are obtained by different methods depending on the fuel cycle.

First, for the initial core, the SAM is determined using xenon vibration at 20% output and 50% output at the beginning of the cycle. The use of xenon vibration in the initial core is very similar to the output distribution of the core regardless of the output level, and the use of xenon vibration takes about 2 to 3 days.

On the other hand, in case of reloading core, SAM is determined after increasing core output from 20% output to 80% output while maintaining about 3% output evaporation rate through Fast Power Ascension Test (FPA). .

In the reloading core, the axial power distribution varies greatly with power due to axial inhomogeneities in fuel assembly combustion. Thus, in the reload core, the SAM is determined using only 30 to 70 measurements taken during the FPA process without using xenon vibration.

In the reloading core, the axial power distribution varies greatly along the power due to the axial inhomogeneity of the fuel assembly combustion. Thus, in the reload core, the SAM is determined using only 30 to 70 measurements taken during the FPA process without using xenon vibration. Each measurement consists of the output distribution of the core at a specific moment and the output of the off-the-surface instrument at that time, and the outer core output distribution P _i is calculated by a computer program.

If various measurement data are given through xenon vibration or FPA process, SAM is determined by the least-square method. Assuming that N measurement data are given, each element of the SAM for each core protection operator channel is solved using the least square method as shown in Equation 2 below.

x = (A ^T A) ^-1 A ^T b

i means channels A, B, C, D, and superscript means 1, ..., N measurement data.

However, the conventional SAM determination method has the following characteristics and problems.

o A satisfactory SAM cannot be obtained every cycle. When using the current SAM determination method, the accuracy of SAM differs depending on the cycle, and the characteristics of the determined SAM may vary greatly depending on the core protection operator channel. This is mainly due to the noise signal included in the measurement data.

o At the beginning of the cycle, the output distribution is relatively accurate, but as the combustion degree of the core increases, the error of the output distribution increases. This is because the SAM is determined at the beginning of the cycle and applied to the overall combustion degree. Therefore, at the beginning of the cycle, it is necessary to determine a SAM that can sufficiently reflect the physical characteristics of the off-the-shelf instrument, but there is a problem in that there is no methodology for this.

In order to solve the above problems, an object of the present invention is to search for the correct solution by using a Constrained Genetic Algorithm, economical through the improvement of power plant utilization by reducing the downtime of the reload cycle In addition to gains, it is technically to provide a method for determining the SAM of an off-shore instrument that can enhance the safety of the core by enhancing the reliability of the core protection system.

In order to achieve the above object, a method for determining a nuclear power plant off-site instrument SAM using a genetic algorithm according to the present invention is a method for determining a set value (SAM) of an off-site instrument of a nuclear power plant. It provides an optimal physical solution based on an algorithm.

Equation

여기서, λ는 라그랑즈 곱셈 벡터(Lagrange multiplier vector)이며, 벡터 λ의 λi요소는 nonnegative이며 라그랑즈 곱셉 추정치(Lagrange multiplier estimates)이고, 벡터(vector) s는 nonnegative shift, ρ는 positive penalty parameter이다. C(x)는 비선형 부등식(nonlinear inequality)과 등식 제한요소(equality constraints)이고, m과 mt는 각각 비선형 부등식 제한요소(nonlinear inequality constraints)의 수 및 전체 비선형 제한요소(nonlinear constraints)의 수이다.

Here, λ is a Lagrange multiplier vector, λi of the vector λ is nonnegative, Lagrange multiplier estimates, vector s is nonnegative shift, and ρ is a positive penalty parameter. C (x) is nonlinear inequality and equality constraints, and m and mt are the number of nonlinear inequality constraints and the total number of nonlinear constraints, respectively.

And, the objective function applied to the genetic algorithm is characterized in that the following equation.

Equation

여기서, E_i는 i번째 채널의 노심출력과 노외계측기 설정치가 계산한 출력의 오차를 나타내며, P_i는 i번째 채널에 인접한 노심외곽 상, 중, 하 출력을 나타내며, D_i는 i번째 채널의 노외계측기 상, 중, 하 신호를 나타내며, S_ij는 노외계측기의 설정치 (Shape Annealing MatrixSAM)를 나타낸다.
또한, 상기 유전알고리즘은 시험치(T_V) 4.0과 유사하고, 하기 수학식의 제한행렬 조건을 동시에 만족하는 물리적 해를 산출하는 것을 특징으로 한다.

Where E _i represents the error between the core output of the i-th channel and the output calculated by the external instrument setpoint, P _i represents the upper, middle and lower outputs of the outer core adjacent to the i-channel, and D _i represents the i-channel The upper, middle and lower signals of the outside instrument are shown, and S _ij represents the setting value (Shape Annealing MatrixSAM) of the outside instrument.
In addition, the genetic algorithm is similar to the test value (T _V ) 4.0, characterized in that to calculate a physical solution that simultaneously satisfies the constraint matrix condition of the following equation.

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Equation

여기서, G(Top)행렬은 상부 노외계측기 신호에 대응하는 대각요소 S₁₁은 항상 양이며 S₁₂는 항상 음을 가지게 하는 제한행렬이고, G(Middle)행렬은 중간 노외계측기 신호에 대응하는 대각요소 S₂₂는 항상 양이며 S₂₁과 S₂₃은 항상 음을 가지게 하는 제한행렬이고, G(Bottom)행렬은 하부 노외계측기 신호에 대응하는 대각요소 S₃₃은 항상 양이며 S₃₂는 항상 음을 가지게 하는 제한행렬이다
이하, 본 발명의 구체적인 구성 및 작용에 대해 도면 및 실시예를 참조하여 상세하게 설명하기로 한다.

Here, the G (Top) matrix is the diagonal element S ₁₁ corresponding to the top out-of-measuring instrument signal S ₁₁ is always positive and S ₁₂ is the limiting matrix which always has negative, and the G (Middle) matrix is the diagonal element corresponding to the middle out-of-measure instrument signal S ₂₂ is always positive, S ₂₁ and S ₂₃ are always limiting matrices, G (Bottom) matrix is the diagonal element S ₃₃ corresponding to the lower out-of-band instrument signal S ₃₃ is always positive, and S ₃₂ is always negative Restriction matrix
Hereinafter, the specific configuration and operation of the present invention will be described in detail with reference to the drawings and the embodiments.

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Genetic Algorithm (GA) applied to the present invention is a probabilistic optimal solution search method that mimics the evolution of ecosystems, that is, natural selection and genetic laws. unconstrained) A well-known algorithm for solving optimization problems.

More specifically, the genetic algorithm (GA) searches for the optimal solution by operating a population composed of several individuals in the GA. For each generation, the fitness of each individual in the population is assessed, and on the basis of this, the good individuals are natural selected, and the natural selected individuals combine with each other and cross each other's genotypes. Produce children.

Here, in order for an individual to survive in a given environment, it has to have an optimal goodness of fit, and this optimum value can be obtained by optimizing this by setting a fitness function, which is an objective function, as in the general function of the general optimization problem.

In addition, mutations occur in certain genes of an individual at a given probability, resulting in a change in genotyping. In this process, generational replacement is carried out and newly born individuals are evaluated again. This process continues until certain conditions are met so that individuals in the population evolve to find the optimal solution. Here, selction, crossover and mutation become the genetic operator of the genetic algorithm.

Genetic algorithm as described above is not only a known technique, but also obvious to those skilled in the art will not be described in detail.

In order to obtain the constraints to be applied to the genetic algorithm, the solution of Equation 2 is obtained by solving a least-squares problem as shown in Equation 3 below.

Where || · || ₂ means quadratic norm, x is the independent variable, b is the dependent variable, and A is the correlation coefficient between the independent and dependent variables.

If the matrix (A ^T A) is ill-conditioned, that is, the condition number (defined as ≡ || (A ^T A) || · || (defined by A ^T A) ^-1 ||) is very large, Becomes very sensitive to perturbations in the data.

In other words, even in the presence of very small measurement noise, the area of solution cannot be predicted at all, and in many cases, the result is a region having no physical meaning. When the matrix A has a perfect invertible condition, the condition number becomes 1, and the larger the ill-conditioned property, the greater the increase in the singular matrix.

When solving discrete ill-posed problems, several sub-optimal solutions may exist, depending on the constraints of the solution.

1. If the condition number of the matrix (A ^T A) is large, the influence of the measured noise must be taken into account.

2. Replacing the matrix A ^T A with a well-conditioned matrix derived from it does not necessarily lead to a meaningful (useful) solution.

3. Carefulness is required when applying additional constraints.

SAM is basically a kind of linear transfer operator that connects the core output and the out-of-field instrument. It shows the physical characteristics of the out-of-counter instrument. Therefore, there are some important physical and mathematical characteristics that must be satisfied for SAM to accurately represent the relationship between core and off-site measurement periods.

The characteristics of the SAM can be understood mainly from the inverse matrix point of view. By definition, SAM is an operator that converts out-of-the-meter instrument information into the core output. So fundamentally, SAM corresponds to expressing the physical phenomenon of the response of an off-site instrument in the opposite direction.

After all, in order to understand the characteristics of SAM accurately, it is necessary to analyze the characteristics of SAM's Inverse SAM (ISAM).

ISAM basically describes how the off-site instrument reacts to a given core output distribution. ISAM has the following characteristics according to the physical characteristics of the off-the-shelf instrument. First all elements must be positive. This is because the neutrons in the core have a probability of reacting in the off-the-shelf instrument regardless of their position. In particular, from the point of view of contributions to off-the-counter instruments in three-core cores, such as ISAM, each area clearly has a non-zero importance.

Another important characteristic of ISAM is that the elements that make up each row must satisfy certain inequalities. When the elements of ISAM are referred to as T _ij , there is an inequality between these elements as shown in Equation 4 below.

이다.here,

to be.

The inequality of Equation 4 is based on the characteristics of the out-of-road measuring instrument as follows.

In essence, the signal from the off-the-shelf instrument can be generated only when the neutrons generated in the core reach the instrument through various barriers such as fuel, moderators, barrels, and pressure vessels.

This increases the probability that neutrons generated closer to the instrument will react in the instrument than neutrons generated farther away. Because of these physical properties, the above inequality holds.

As can be seen from Equation 4, ISAM has a so-called Diagonal Dominance characteristic. Of course, the characteristics of the ISAM described above are those assuming an ideal ISAM. In general, the measured SAM inverse does not satisfy all of the characteristics of the ISAM presented above because of measurement data problems or limitations in the determination method itself. However, in order for SAM to be optimal, it must basically satisfy the characteristics of the above ISAM.

The above characteristics of ISAM mean that the following characteristics must exist from SAM perspective.

1) Diagonal elements must be positive.

2) Diagonal dominance must be satisfied.

The diagonal dominance of SAM can be evaluated in two ways.

First, as defined, the diagonal of a row must be greater than the sum of the absolute values of the remaining non-diagonal elements. Diagonal dominance in this respect is characteristic for each off-channel instrument subchannel.

In this regard, constraints can be placed on the SAM matrix.

When S ₁₂ , one of the upper diagonal elements, is calculated in Equation 4, S ₁₂ = T ₁₃ T ₃₂ -T ₁₂ T ₃₃ <0. Because T ₁₃ <T ₁₂ ~ T ₃₂ ≪T ₃₃ , S ₁₂ must be negative. Similarly, S ₂₁ , S ₃₂ and S ₁₃ should always be negative.

This constraint is always a convincing condition because it is a physical constraint that must be met by an off-the-shelf instrument that sees the output of the furnace.

Therefore, in the calculation of the SAM matrix, each constraint matrix for the upper, middle, and lower parts of the measuring instrument is expressed by Equation 5 below.

여기서, G(Top)행렬은 상부 노외계측기 신호에 대응하는 대각요소 S₁₁은 항상 양이며 S₁₂는 항상 음을 가지게 하는 제한행렬이고, G(Middle)행렬은 중간 노외계측기 신호에 대응하는 대각요소 S₂₂는 항상 양이며 S₂₁과 S₂₃은 항상 음을 가지게 하는 제한행렬이고, G(Bottom)행렬은 하부 노외계측기 신호에 대응하는 대각요소 S₃₃은 항상 양이며 S₃₂는 항상 음을 가지게 하는 제한행렬이다

Here, the G (Top) matrix is the diagonal element S ₁₁ corresponding to the top out-of-measuring instrument signal S ₁₁ is always positive and S ₁₂ is the limiting matrix which always has negative, and the G (Middle) matrix is the diagonal element corresponding to the middle out-of-measure instrument signal S ₂₂ is always positive, S ₂₁ and S ₂₃ are always limiting matrices, G (Bottom) matrix is the diagonal element S ₃₃ corresponding to the lower out-of-band instrument signal S ₃₃ is always positive, and S ₃₂ is always negative Restriction matrix

Currently, the diagonal dominance of the SAM matrix is evaluated in terms of the so-called Test Value (T _V ) in the case of the Korean standard nuclear power plant. T _V is the sum of the absolute values of all elements of the matrix given by the product of the SAM and ISAM diagonal elements and the SAM, and according to the current procedure, the relationship is satisfied.

T _V The value depends on the characteristics of the out-of-counter instrument, and a particularly significant factor is the distance between the out-of-counter instrument and the pressure vessel. If the off-site instrument is very close to the pressure vessel, most of the off-site instrument signal will be generated by neutrons leaking from the core adjacent to the off-site instrument. In other words, as the distance from the instrument to the top or bottom of the core, the contribution of the region to the off-site instrument rapidly decreases.

However, if the out-of-counter instrument is considerably far from the pressure vessel, the core's importance will not be very sensitive depending on the height of the core. It can be said that the upper limit and the lower limit of the value are determined based on such physical phenomenon. As a result, the T _V value may vary depending on the design of the off-the-shelf instrument.

In the case of the Korean standard nuclear power plant, the previous experience shows that the optimum value is around 4.0. In other words, the value is similar to 4.0 when the SAM is optimally determined and the error of the core protection operator output distribution is small. However, the fact that the value is similar to 4.0 does not always mean that SAM is optimal. That is, it is most preferable that the value is similar to 4.0 and satisfies the constraint G of Equation 5 above, and the methodology presented in the present invention is always limited by searching for a solution using a genetic algorithm having this constraint. Provides an accurate solution to meet

The objective function applied to the genetic algorithm is defined as the following Equation 6 as an error between the core output and the output calculated by the instrument using the SAM.

여기서　 i 와 j 는 각각 1,2,3 으로 계측기의 상부, 가운데, 하부위치를 의미하고, E_i는 i번째 채널의 노심출력과 노외계측기 설정치가 계산한 출력의 오차를 나타내며, P_i는 i번째 채널에 인접한 노심외곽 상, 중, 하 출력을 나타내며, D_i는 i번째 채널의 노외계측기 상, 중, 하 신호를 나타내며, S_ij는 노외계측기의 설정치 (Shape Annealing MatrixSAM)를 나타낸다.

Where i and j are 1,2,3 , respectively, which means the upper, middle and lower positions of the instrument, E _i represents the error of the core output of the i-th channel and the output calculated by the set value of the external instrument, and P _i is i The upper, middle and lower outputs of the core adjacent to the first channel are shown, D _i represents the upper, middle and lower signals of the out-of-measuring instrument of the i-th channel, and S _ij represents the setting value (Shape Annealing MatrixSAM) of the outside instrument.

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The optimal solution using the genetic algorithm is obtained by searching for a solution that minimizes the objective function defined in Equation 6 above.

In other words, genetic operators of genetic algorithms (selection, crossover and mutation) are applied to the set of possible solutions to search for the minimum objective function.

The method applied to the present invention is applied to the problem of nonlinear optimization with constraints with an extended Augmented Lagrangian Genetic Algorithm (ALGA).

In other words, the objective function and the constraints are combined as shown in Equation 7 below.

Here, lambda is a Lagrange multiplier vector, and the lambda i element of the vector lambda is nonnegative and is known as Lagrange multiplier estimates.

Vector s is a nonnegative shift and ρ is a positive penalty parameter. C (x) is nonlinear inequality and equality constraints. m and mt are the number of nonlinear inequality constraints and the total number of nonlinear constraints, respectively.

The algorithm starts by using the initial value of the penalty parameter and when the equation 7 is minimized to the exact value required and satisfies feasibility conditions, Lagrangian estimates are obtained. Upgrade

Otherwise, the penalty parameter is increased by the penalty factor, resulting in new constraints and minimization problems.

This step is performed repeatedly until the constraint is satisfied.

That is, by applying a fitness fuction as shown in Equation 7 to the genetic algorithm GA, the process of repeatedly selecting the solution to minimize the objective function is naturally selected by violating the constraint. You get harm.

Out-of-measurement instrument SAM determination method according to the present invention by using the actual measurement data and the result of applying the present invention to the SAM determination process and the magnitude of the measurement error that occurs as the process proceeds compared to the existing methodology, the effect of the present invention and the superiority of the new methodology It was confirmed.

Table 1 below shows the existing SAM determination methodology and the "method for determining the out-of-measurement instrument SAM of a nuclear power plant using normalization and inverse matrix constraints" (registration date 2006-01-26, registration number 0549339) and the present invention, which are proposed as prior patents The performance comparison of the calculated SAM.

Channel Test values Existing Methodology Prior Patent The present invention A 4.6149 3.8829 4.0849 B 20.1500 3.8986 4.0466 C 10.0038 3.7313 4.1244 D 29.3876 3.9829 4.1474

As can be seen through Table 1, the out-of-measurement instrument SAM determination method according to the present invention provides excellent results that the T _V value is very close to 4.0.

3 is a comparison result of tracking the error of the axial output distribution calculated using the present SAM calculation methodology and the present invention from the reactor cycle beginning to the end of the cycle.

Referring to FIG. 3, when the conventional method does not provide accurate SAM, it can be seen that the calculation method of the present invention is greatly improved in accuracy as the cycle progresses. This is because the calculation method of the present invention provides an accurate SAM that is physically meaningful.

As described above, the SAM determination method of the off-site instrument of the nuclear power plant using the genetic algorithm according to the present invention, by searching the physically accurate solution, as well as the economic benefit through the improvement of the utilization rate of the plant by shortening the operating time of the reload cycle, In addition, an excellent effect of enhancing the reliability of the core protection system can be achieved.

Although the detailed description of the present invention described above has been described with reference to the preferred embodiment of the present invention, the protection scope of the present invention is not limited to the above embodiment, and those skilled in the art will appreciate It will be understood that various modifications and changes can be made in the present invention without departing from the spirit and scope of the invention.

Claims (3)

In the method of determining the set value (SAM) of the off-road instrument of a nuclear power plant, Method for determining an off-shore instrument SAM of a nuclear power plant using a genetic algorithm, characterized in that to provide an optimal physical solution based on a genetic algorithm having a constraint such as the following equation. Equation

Here, λ is a Lagrange multiplier vector, λi of the vector λ is nonnegative, Lagrange multiplier estimates, vector s is nonnegative shift, and ρ is a positive penalty parameter. C (x) is nonlinear inequality and equality constraints, and m and mt are the number of nonlinear inequality constraints and the total number of nonlinear constraints, respectively. The method of claim 1, The objective function applied to the genetic algorithm is a nuclear power plant off-site instrument SAM determination method using a genetic algorithm, characterized in that the following equation. Equation

Where E _i represents the error between the core output of the i-th channel and the output calculated by the external instrument setpoint, P _i represents the upper, middle and lower outputs of the outer core adjacent to the i-channel, and D _i represents the i-channel The upper, middle and lower signals of the outside instrument are shown, and S _ij represents the setting value (Shape Annealing MatrixSAM) of the outside instrument. The method of claim 1, The genetic algorithm is similar to the test value (T _V ) 4.0, and calculates a physical solution that satisfies the constraint matrix condition of the following equation simultaneously, characterized in that the nuclear power plant off-site instrument SAM determination method. Equation

Here, the G (Top) matrix is the diagonal element S ₁₁ corresponding to the top out-of-measuring instrument signal S ₁₁ is always positive and S ₁₂ is the limiting matrix which always has negative, and the G (Middle) matrix is the diagonal element corresponding to the middle out-of-measure instrument signal S ₂₂ is always positive, S ₂₁ and S ₂₃ are always limiting matrices, G (Bottom) matrix is the diagonal element S ₃₃ corresponding to the lower out-of-band instrument signal S ₃₃ is always positive, and S ₃₂ is always negative Constraint matrix.

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